complementary input that are fundamental to agroecological simulation models, but permit
more insight into the available options for factor substitution in which economists are primarily
interested. Moreover, an even wider range of in- put – output coefficients becomes available that
enhances the stability of the model and prevents the occurrence of corner solutions. Finally, the
estimated functions still include all points of tech- nical efficiency but enable a more detailed analysis
of marginal effects.
The performance of meta-models demonstrates in practice a number of problems related to the
typical distribution of observations and error terms. Since most meta-models are derived from
rather deterministic simulation procedures, prob- lems with heteroscedasticity and serial correlation
frequently appear. Therefore, Durbin – Watson statistics and the White test should be carefully
analysed. The relative prediction error can be calculated, based on the percentage change in the
forecasted value of the regression function when one observation is deleted. Other problems arise
when joint output is considered in the meta-model e.g. yields and nutrient balances. In this article
we calculated the environmental implications of selected input – output coefficients by using again
the original agroecological data. In principle, both yields and environmental effects could also be
estimated simultaneously using two-stage least square 2SLS procedures Pindyck and Ru-
binfeld, 1991. Otherwise, parametric distance functions might offer a suitable alternative Rein-
hard and Thijssen, 1998.
5. Results
To explore the potential of meta-modelling for bio-economic household modelling, the procedure
is applied to the production side of a bio-eco- nomic farm household model for Koutiala region
in Southern Mali Kruseman and Bade, 1998. The original data for the meta-model consist of a
series of discrete technical input – output coeffi- cients for current and alternative or potential
production activities. These coefficients stem in turn from the agroecological simulation model.
The meta-model can be optimised within a mathe- matical programming framework. Optimisation
takes place for the farm household objective of consumption utility.
The meta-modelling approach is applied to this series of several hundreds of data points for all
crop and livestock activity to derive continuous production functions for each activity, making use
of the Battese 1996 procedure to account for zero input use. For arable cropping, we estimated
the
following Cobb – Douglas
production function
3
: lnY = b
+ b
1
lnL + b
2
lnT + b
3
lnN + b
4
lnP + b5 lnM 1
where Y represents the quantity of the different harvested crops in monetary units, L and T are
the total amounts of labour and traction in working days; N and P are the amounts of active
ingredients of nitrogen and phosphorous fertilis- ers applied to the crop in kgha; and M is the
amount of manure applied in kgha. Table 1 shows the results of the production functions for
cropping activities using the White correction for heteroscedasticity.
The results of the estimated functions are ac- ceptable. All but a few signs for inputs are posi-
tive and those negative are not significant. The coefficients for labour are positive and significant,
and especially in cotton and cowpea production the elasticity of labour is high. This is consistent
with the scarcity of labour in the research area. The traction elasticities for cereals and cotton are
estimated between 0.06 and 0.20, while for cowpea and groundnut these are estimated to be
about 0.7. The valid coefficients for different types of fertilisers are lower than 0.3; for sor-
ghum, cowpea and groundnut the fertiliser coeffi- cients are, however, not significant. The negative
coefficients for manure in millet and cowpea pro- duction are difficult to explain since it is common
3
The Cobb-Douglas functional form is used for its relative simplicity and because it provided the best fit in the analysis.
Other functional forms translog, quadratic produced a singu- lar matrix. Given the synergy effects involved in agroecological
simulation, a quadratic specification would have been pref- ered.
R .
Ruben ,
A .
6 an
Ruij 6
en Ecological
Economics
36 2001
427 –
441
435 Table 1
Cobb–Douglas production functions for cropping activities Coefficients and t-statistics using OLS regression Sorghum
Cowpea Groundnut
Maize Cotton
Millet t-stat
Coef. t-Stat
Coef. t-stat
Coef. Coef.
t-stat Coef.
t-stat Coef.
t-stat −
9.39 1.62
3.95 1.11
14.51 −
2.97 −
3.13 1.40
1.03 c
5.72 1.47
− 4.05
9.60 0.14
8.92 1.83
8.19 0.74
0.86 2.47
0.97 Labour
20.61 1.94
16.97 0.20
0.16 7.59
0.06 13.2
0.75 17.6
0.67 10.7
8.67 0.13
5.07 Traction
7.74 −
0.01 −
0.82 −
0.03 −
1.32 −
0.02 N fertiliser
− 0.55
0.10 5.35
0.09 3.34
0.20 1.77
0.01 1.28
0.10 0.23
0.02 0.05
0.13 P fertiliser
8.07 0.09
14.24 0.25
− 1.39
0.01 2.86
− 0.12
− 5.48
− 0.04
Manure −
1.64 0.06
8.58 0.07
7.27 −
0.02 309
192 168
273 192
309 N
a
Adj. R
2
0.88 0.95
0.81 0.77
0.93 0.89
0.77 0.91
0.82 0.73
D-W
a
1.23 1.07
0.55 RPE
a
3.71 2.30
3.20 1.20
0.97
a
N is the number of observations; D-W is the Durbin–Watson statistic; and RPE is the relative prediction error in PB0.05.
PB0.01. PB0.001
Table 2 Linear production functions for meat and milk production
a
Milk Meat
t-stat Coef.
t-stat Coef.
− 516
− 7.16
Constant 166
− 1346
6.85 q1
0.99 0.20
0.54 q2
0.19 1.16
0.18 0.56
7.46 q3
1.26 5.26
0.46 q4
0.17 1.38
0.16 0.49
6.24 q5
1.54 7.24
0.52 q6
0.15 1.69
0.14 0.56
8.34 q7
1.80 9.37
0.60 q8
0.13 1.93
0.13 0.63
10.1 q9
2.10 0.69
q10 2.40
0.13 11.0
0.70 Adjusted R
2
0.92 0.19
Durbin–Watson Stat. 0.17
96 Number of observations
96
a
q1…q10 are food categories of different qualities. In the function for meat q1 and q2 are estimated together. PB0.001.
understanding that additional manure should have a neutral or positive influence on crop yield.
Apparently, input efficiency of nutrients derived from organic manure is rather limited compared
to chemical fertilisers Ruben and Lee, 2000. Moreover, part of the nutrients from organic
manure may become immobilised into lower soil- layers. The production function for groundnut
has the lowest R
2
and only two coefficients are significant. All functions for crop production have
increasing returns to scale, as can be derived from the sum of the individual input elasticities. The
Durbin – Watson statistics
are relatively
low, probably due to serial correlation related to the
fixed soil-input relations in the agroecological simulation model.
4
Livestock activities are defined for meat and milk production under different regimes of animal
feeding. These feeding categories are related to the maintenance requirements and the needs for pro-
duction, taking into account the feed source pas- ture, crop residues, cotton cake and quality
N-content and digestible organic matter of dif- ferent feed types. We used the following linear
specification for the production function of livestock:
ln Y = b + b
1
q1 + b
2
q2 …… b
10
q10 2
where q1…q10 represent feed sources available during the wet and dry season that correspond to
different levels of energy intake and digestible organic matter. In Table 2 the results for the
functions for meat and milk production are shown.
The coefficients in Table 2 are all positive and most of them are significant at the 99 level,
except for the constants. The negative constant can be explained by the fact that cattle needs feed
for maintenance, which does not contribute di- rectly to production. Only above a certain level of
food intake do cattle start producing milk and meat. The variables q1 and q2 in the equation of
meat could be estimated together, as the Wald test indicates that they were not significantly different
4
Attempts were made to include a dummy for different soil types to reduce serial correlation, but this did not improve the
D-W statistics.
Table 3 Land use pattern, input use and farm household profit and investment under the assumption of perfect markets and with different
market constraints
a
Land use ha Missing markets
Meat Maize
Sorghum Millet
Cotton Cowpea
Fallow Milk
1931 None base run
3200 3.6
3.6 6.3
4.5 1.8
770 Labour
3.6 3200
6.3 6.3
3200 907
Capital 2.8
2.5 6.3
6.3 3200
Traction 3.6
3.6 6.3
4.5 1964
Profit 10
3
Investment Labour days
Traction days 10
3
None base run 2047
834 3410
157 Labour
1629 634
1800 313
Capital 1750
600 2282
192 Traction
2042 849
3500 120
a
All crops in hectares, meat and milk in kg; profit and investment in Fcfa.
from each other. The adjusted R
2
value is very high which indicates a good fit. However, the
Durbin – Watson statistics indicate that in these functions positive serial correlation occurs.
The estimated functions for crop and animal production are incorporated into a non-linear bio-
economic farm household model Bade et al., 1997; Kruseman and Bade, 1998 which is opti-
mised for the objective of expected utility of con- sumption, given the availability of resources
land, labour, traction:
Max EU = S u·C Y−p
e
·E 3
s.t. Y = p
i
·I + p
c
·C + p
l
·L 4
where C represents a vector of consumption goods, Y represents income derived from pro-
duction, I represents the different inputs, L is labour force, and p are their respective prices. The
vector E includes environmental externalities e.g. nutrient losses valued against their replacement
costs. For optimisation the standard Gams soft- ware is used. When market constraints are effec-
tive, this implies that only resources available at the farm household can be used. In the base run,
households can fully rely on purchased inputs as long as their budget permits. After optimising the
household model, soil nutrient and organic matter balances are calculated for the selected technical
coefficients as major indicators for the sustainabil- ity and resilience of the system Hengsdijk et al.,
1996.
5
The household model is first optimised under the assumption of perfect markets, allowing for
separability and thus sequential optimisation Singh et al., 1986. This base run of the model is
used as a reference point. Subsequently, con- straints are imposed on the labour, capital and
animal traction market by limiting the use of these inputs to the quantities owned by house-
holds. The model specifications with different market imperfections are optimised in a non-sepa-
rable way, which means that the production and consumption part are estimated simultaneously
Delforce, 1994. In Table 3, the model outcomes under the assumptions of perfect and missing
markets are presented.
Table 3 demonstrates that missing markets di- minish the production of crops and meat consid-
erably. The labour market constraint causes a shift from millet production towards less labour-
intensive fallow and cowpea activities, while the area for maize production is maintained. Conse-
quently, less crop residues are available for meat
5
In this model different nutrient loss and supply processes are quantified and — in combination with production levels
and input use — soil nutrient balances are estimated.
Table 4 Consumption of different goods as percentage of total per capita income
Missing market Consumption of per capita income
Meat Milk
Cereals Legumes
Others Utility
2.5 2.3
0.8 27.0
67.4 None base run
715 2.3
2.2 0.8
Labour 65.4
28.7 528
2.3 2.2
0.8 33.0
65.5 Capital
593 2.5
2.3 Traction
0.8 27.0
67.5 714
production. The market constraint for capital causes a shift from maize and millet production to
less input-intensive cowpea production and fal- low, occasioning a similar decline of crop residues
for meat production. With a restriction on the market for animal traction the original land use
pattern is maintained, but production activities become far more labour- and input-intensive.
The introduction of market imperfections re- duces the level of profit due to changes in the land
use pattern andor shifts in production technolo- gies. Missing markets for labour and capital
clearly reduce their factor intensity in the produc- tion process. Apparently, animal traction and
labour can be used as substitutes: with a missing labour market the use of animal traction rises
sharply, while the use of labour increases when constraints for animal traction are imposed. In
principle, when different market imperfections co- incide, possibilities for factor substitution will fur-
ther decrease.
The utility levels for the four different model specifications behave consistently. With market
imperfections utility decreases compared to the situation with perfect markets. Table 4 shows the
results for the consumption side of the model.
Consumption of all categories of goods is lower when market constraints are taken into consider-
ation. The shift from meat consumption towards cereals if per capita income falls is consistent with
consumer demand theory where meat is normally considered as a luxury good. Consequently, a
decrease in income will cause a more than propor- tional fall in meat consumption. Cereals are con-
sidered to be basic requirements for food security and therefore cereal consumption does not de-
crease as much as meat consumption. The implications of market imperfections for
the soil quality under different production systems can be reviewed through the calculation of nutri-
ent balances. Whereas differences in nutrient bal- ances between various cropping activities are
large, the deviations between the model specifica- tions are relatively small. This can be explained by
the fact that the yields per hectare and fertiliser use per hectare differ only slightly between the
models with market imperfections. Consequently, nutrient balances are relatively stable as well. The
influence of labour and capital market imperfec- tions is most pronounced in the increase of fallow.
In this case, market imperfections have a general ‘positive’ effect on sustainability, though at the
expense of a decreasing farm household income. Table 5 shows soil nutrient balances under differ-
ent market conditions:
For policy purposes, we are interested in analysing the effects of higher factor prices result
from structural adjustment programmes on input use and farm household profit. Table 6 shows the
effects of price increases for N-fertiliser and ani- mal traction in order to review the responsiveness
of the bio-economic farm household model. A 10 increase of N-fertiliser results in small de-
Table 5 Nutrient balances in optimal solutions kgha
a
N-balance P-balance
C-balance Missing market
− 4.1
None base run −
1752 −
27 −
1400 −
3.8 Labour
− 24
− 22
Capital −
3.4 −
1401 Traction
− 26
− 1743
− 3.7
a
N is nitrogen, P is phosphorous and C is the organic matter balance.
Table 6 Implications of a 10 increase of N-fertiliser price and animal
traction
a
Indicator Animal traction
Nitrogen Profit
− 0.34
− 0.19
Animal traction −
5.7 –
0.5 –
Labour −
8.0 Nitrogen
– –
2.0 Phosphorous
Manure –
2.2
a
Figures give percentage change in indicator values com- pared to the base run.
6. Discussion and conclusions
